Title: On a property of 2-connected graphs and Dirac's Theorem
Abstract: We refine a property of 2-connected graphs described in the classical paper of Dirac from 1952 and use the refined property to somewhat shorten Dirac's proof of the fact that each 2-connected n-vertex graph with minimum degree at least k has a cycle of length at least min{n,2k}. This is joint work with Alexandr Kostochka and Ruth Luo.
